One woman asked why Ramadan, the Muslim month of fasting, changes dates every year. Then came a question about how Muslims calculate that the world is entering the year 1434.

For Abdelrahman Binjalloun, a Moroccan-born pharmacist who doubles as a guide, the questions were routine. Since it was inaugurated last September after a three-decade controversy – and even while it was under construction – the Great Mosque of Strasbourg has become a tourist site, a destination for school excursions and a meeting place where French people come face to face with their increasingly numerous Muslim neighbours.

Such coming together is not the norm in France, whose army has been dispatched to Mali to destroy bands of radical Islamists who hold 15 French citizens hostage. At home Christian traditions have been rubbed the wrong way by a Muslim minority that is often so concentrated in certain suburban neighbourhoods that veils are common and Arabic is more spoken than French. A law banning full-face veils for women was passed two years ago, one much discussed symptom of the unease, and rightwing political leaders have opposed mosque projects in a number of cities, including Strasbourg.

The number of Muslims in France has never been established with certainty But the interior ministry and mainline researchers have estimated that more than 5 million people, 8% to 10% of the population, were born into families of Muslim tradition. Whatever the exact tally, Muslims have become an increasingly visible part of life in France, and the $14m Great Mosque of Strasbourg has added dramatically to that visibility.

Conceived by an Italian architect, Paolo Portoghesi, the mosque's imposing prayer hall, covered by a copper dome and flanked by soaring wings designed to suggest a blooming flower, has become a familiar landmark beside a graceful curve in the Ill river, near the tourist-heavy Petite France neighbourhood of Strasbourg. More than 20,000 visitors inspected the construction site between July 2011 and July 2012. In the four months since interior minister Manuel Valls and Morocco's religious affairs minister, Ahmed Toufiq, presided over the inauguration, another 10,000 have taken guided toursof the finished building and the tempo of visits is accelerating, according to Said Aalla, a Strasbourg jurist who is president of the mosque's governing council. As word of the mosque and its open-arms policy spreads, tourists have begun asking for directions at the Strasbourg Tourism Office, which sits in the shadow of the medieval cathedral, Notre Dame of Strasbourg, that has long dominated the landscape of the much fought over city of 450,000 on the border between France and Germany.

Aalla said the mosque's secondary vocation as a public monument did not evolve accidentally. He and fellow members of the governing council, he explained, decided early on that if Strasbourg's estimated 40,000 Muslims were to live comfortably with Christian neighbours they had the duty to explain their religion and make it less forbidding. "From the very beginning, we wanted to be open to the people around us," he said.

A group escorted around the mosque on a recent day by Aalla and Binjalloun included about 35 alumni of a Roman Catholic engineering school, along with family members, and several of the school's Dominican professors in cream-coloured friars' robes. "I have long been interested in the Muslim world," said one of them, the Rev Benoit Ente, who spent two years as an aid worker in heavily Muslim Chad. "I was very interested to know what this mosque is like."

After deciphering the Arabic-script Qur'anic verses decorating a frieze around the hall, Binjalloun pointed out that the mosque contains no images of God or Muhammad, in accordance with Islamic strictures. But, he added, it also contains none of the arcades common to Moroccan or other Middle Eastern architecture, because Portoghesi's design was conceived for construction in Europe for European Muslims.

"From the beginning, we wanted a project for Strasbourg and for Europe," Binjalloun told the visitors.

As for the calendar, he said, it is based on lunar calculations, which explains why a Muslim year is different from the Gregorian calendar used by Christians and why Ramadan begins on a different date every year.

Although a symbol of ecumenism now, the Great Mosque of Strasbourg also has been an example of the tensions surrounding France's growing Muslim minority. Under discussion since the late 1970s, it almost did not get built. By the time it did, the project had been truncated. "The history of the Great Mosque was long, difficult and tortuous," said Olivier Bitz, deputy mayor in charge of religious affairs in the Socialist-run Strasbourg city council, headed by mayor Roland Ries. After 15 years of fruitless meetings and conferences between Muslim figures and city officials, then-mayor Catherine Trautmann in 1993 decided that the mosque would be built on a grand scale and that the city would help in the financing. Her decision, a departure strongly opposed by conservatives, was a major campaign issue in the 1995 elections that brought her Socialist majority to power for another term.

By 2000, the decision was enshrined in law, the city-owned plot was leased under favourable conditions and contracts were negotiated with Portoghesi.

A conservative coalition captured city hall in 2001 under then-mayor Fabienne Keller and, according to Bitz, set out to bury the mosque.

"The entire project was put into question," he said.

Prodded by far-right National Front objections, Keller's mainstream right council vetoed plans for a minaret – the distinctive architectural spire common to mosques – a cultural centre and a tea salon. It shrank plans for the prayer hall by a third, forbade an underground car park and banned donations by foreign countries or sermons in Arabic.

At the same time, dissension erupted among Muslims. Those from Algeria and Tunisia complained that immigrants from Morocco, the largest segment of the Muslim community, were monopolising decisions on the strength of promises of financial aid from the Moroccan government.

The project in theory started in 2004 But it was mired in discord and went nowhere. Construction got off the ground only with the arrival in 2008 of a socialist administration, this oneunder Ries. With his blessing, fundraising resumed, with the price tag having risen to just under $14m: 26% came from city hall and the regional council, 33% from local donations and 37% from Morocco. The rest came from Saudi Arabia and Kuwait. Now that the mosque is finished, and Ries has erased the restrictions, Aalla said Portoghesi has been asked to design an extension. It will embrace the originally planned cultural centre, the tea salon, and perhaps even a minaret. Unless, Bitz cautioned, Ries is voted out before they can be completed.

• This article appeared in Guardian Weekly, which incorporates material from the Washington Post